impls/bddc/bddcfetidp.c

#include <petsc/private/pcbddcimpl.h>
#include <petsc/private/pcbddcprivateimpl.h>
#include <petscblaslapack.h>

static PetscErrorCode MatMult_BDdelta_deluxe_nonred(Mat A, Vec x, Vec y)
{
  BDdelta_DN ctx;

  PetscFunctionBegin;
  PetscCall(MatShellGetContext(A, &ctx));
  PetscCall(MatMultTranspose(ctx->BD, x, ctx->work));
  PetscCall(KSPSolveTranspose(ctx->kBD, ctx->work, y));
  /* No PC so cannot propagate up failure in KSPSolveTranspose() */
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatMultTranspose_BDdelta_deluxe_nonred(Mat A, Vec x, Vec y)
{
  BDdelta_DN ctx;

  PetscFunctionBegin;
  PetscCall(MatShellGetContext(A, &ctx));
  PetscCall(KSPSolve(ctx->kBD, x, ctx->work));
  /* No PC so cannot propagate up failure in KSPSolve() */
  PetscCall(MatMult(ctx->BD, ctx->work, y));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode MatDestroy_BDdelta_deluxe_nonred(Mat A)
{
  BDdelta_DN ctx;

  PetscFunctionBegin;
  PetscCall(MatShellGetContext(A, &ctx));
  PetscCall(MatDestroy(&ctx->BD));
  PetscCall(KSPDestroy(&ctx->kBD));
  PetscCall(VecDestroy(&ctx->work));
  PetscCall(PetscFree(ctx));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PCBDDCCreateFETIDPMatContext(PC pc, FETIDPMat_ctx *fetidpmat_ctx)
{
  FETIDPMat_ctx newctx;

  PetscFunctionBegin;
  PetscCall(PetscNew(&newctx));
  /* increase the reference count for BDDC preconditioner */
  PetscCall(PetscObjectReference((PetscObject)pc));
  newctx->pc     = pc;
  *fetidpmat_ctx = newctx;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PCBDDCCreateFETIDPPCContext(PC pc, FETIDPPC_ctx *fetidppc_ctx)
{
  FETIDPPC_ctx newctx;

  PetscFunctionBegin;
  PetscCall(PetscNew(&newctx));
  /* increase the reference count for BDDC preconditioner */
  PetscCall(PetscObjectReference((PetscObject)pc));
  newctx->pc    = pc;
  *fetidppc_ctx = newctx;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PCBDDCDestroyFETIDPMat(Mat A)
{
  FETIDPMat_ctx mat_ctx;

  PetscFunctionBegin;
  PetscCall(MatShellGetContext(A, &mat_ctx));
  PetscCall(VecDestroy(&mat_ctx->lambda_local));
  PetscCall(VecDestroy(&mat_ctx->temp_solution_D));
  PetscCall(VecDestroy(&mat_ctx->temp_solution_B));
  PetscCall(MatDestroy(&mat_ctx->B_delta));
  PetscCall(MatDestroy(&mat_ctx->B_Ddelta));
  PetscCall(ISDestroy(&mat_ctx->lP_I));
  PetscCall(ISDestroy(&mat_ctx->lP_B));
  PetscCall(MatDestroy(&mat_ctx->B_BB));
  PetscCall(MatDestroy(&mat_ctx->B_BI));
  PetscCall(MatDestroy(&mat_ctx->Bt_BB));
  PetscCall(MatDestroy(&mat_ctx->Bt_BI));
  PetscCall(MatDestroy(&mat_ctx->C));
  PetscCall(VecDestroy(&mat_ctx->rhs_flip));
  PetscCall(VecDestroy(&mat_ctx->vP));
  PetscCall(VecDestroy(&mat_ctx->xPg));
  PetscCall(VecDestroy(&mat_ctx->yPg));
  PetscCall(VecScatterDestroy(&mat_ctx->l2g_lambda));
  PetscCall(VecScatterDestroy(&mat_ctx->l2g_lambda_only));
  PetscCall(VecScatterDestroy(&mat_ctx->l2g_p));
  PetscCall(VecScatterDestroy(&mat_ctx->g2g_p));
  PetscCall(PCDestroy(&mat_ctx->pc)); /* decrease PCBDDC reference count */
  PetscCall(ISDestroy(&mat_ctx->pressure));
  PetscCall(ISDestroy(&mat_ctx->lagrange));
  PetscCall(PetscFree(mat_ctx));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PCBDDCDestroyFETIDPPC(PC pc)
{
  FETIDPPC_ctx pc_ctx;

  PetscFunctionBegin;
  PetscCall(PCShellGetContext(pc, &pc_ctx));
  PetscCall(VecDestroy(&pc_ctx->lambda_local));
  PetscCall(MatDestroy(&pc_ctx->B_Ddelta));
  PetscCall(VecScatterDestroy(&pc_ctx->l2g_lambda));
  PetscCall(MatDestroy(&pc_ctx->S_j));
  PetscCall(PCDestroy(&pc_ctx->pc)); /* decrease PCBDDC reference count */
  PetscCall(VecDestroy(&pc_ctx->xPg));
  PetscCall(VecDestroy(&pc_ctx->yPg));
  PetscCall(PetscFree(pc_ctx));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PCBDDCSetupFETIDPMatContext(FETIDPMat_ctx fetidpmat_ctx)
{
  PC_IS          *pcis      = (PC_IS *)fetidpmat_ctx->pc->data;
  PC_BDDC        *pcbddc    = (PC_BDDC *)fetidpmat_ctx->pc->data;
  PCBDDCGraph     mat_graph = pcbddc->mat_graph;
  Mat_IS         *matis     = (Mat_IS *)fetidpmat_ctx->pc->pmat->data;
  MPI_Comm        comm;
  Mat             ScalingMat, BD1, BD2;
  Vec             fetidp_global;
  IS              IS_l2g_lambda;
  IS              subset, subset_mult, subset_n, isvert;
  PetscBool       skip_node, fully_redundant;
  PetscInt        i, j, k, s, n_boundary_dofs, n_global_lambda, n_vertices, partial_sum;
  PetscInt        cum, n_local_lambda, n_lambda_for_dof, dual_size, n_neg_values, n_pos_values, buf_size;
  PetscMPIInt     rank, size, neigh;
  PetscScalar     scalar_value;
  const PetscInt *vertex_indices;
  PetscInt       *dual_dofs_boundary_indices, *aux_local_numbering_1;
  const PetscInt *aux_global_numbering;
  PetscInt       *aux_sums, *cols_B_delta, *l2g_indices;
  PetscScalar    *array, *scaling_factors, *vals_B_delta;
  PetscScalar   **all_factors;
  PetscInt       *aux_local_numbering_2;
  PetscInt       *count, **neighbours_set;
  PetscLayout     llay;

  /* saddlepoint */
  ISLocalToGlobalMapping l2gmap_p;
  PetscLayout            play;
  IS                     gP, pP;
  PetscInt               nPl, nPg, nPgl;

  PetscFunctionBegin;
  PetscCall(PetscObjectGetComm((PetscObject)fetidpmat_ctx->pc, &comm));
  PetscCallMPI(MPI_Comm_rank(comm, &rank));
  PetscCallMPI(MPI_Comm_size(comm, &size));

  /* saddlepoint */
  nPl      = 0;
  nPg      = 0;
  nPgl     = 0;
  gP       = NULL;
  pP       = NULL;
  l2gmap_p = NULL;
  play     = NULL;
  PetscCall(PetscObjectQuery((PetscObject)fetidpmat_ctx->pc, "__KSPFETIDP_pP", (PetscObject *)&pP));
  if (pP) { /* saddle point */
    /* subdomain pressures in global numbering */
    PetscCall(PetscObjectQuery((PetscObject)fetidpmat_ctx->pc, "__KSPFETIDP_gP", (PetscObject *)&gP));
    PetscCheck(gP, PETSC_COMM_SELF, PETSC_ERR_PLIB, "gP not present");
    PetscCall(ISGetLocalSize(gP, &nPl));
    PetscCall(VecCreate(PETSC_COMM_SELF, &fetidpmat_ctx->vP));
    PetscCall(VecSetSizes(fetidpmat_ctx->vP, nPl, nPl));
    PetscCall(VecSetType(fetidpmat_ctx->vP, VECSTANDARD));
    PetscCall(VecSetUp(fetidpmat_ctx->vP));

    /* pressure matrix */
    PetscCall(PetscObjectQuery((PetscObject)fetidpmat_ctx->pc, "__KSPFETIDP_C", (PetscObject *)&fetidpmat_ctx->C));
    if (!fetidpmat_ctx->C) { /* null pressure block, compute layout and global numbering for pressures */
      IS Pg;

      PetscCall(ISRenumber(gP, NULL, &nPg, &Pg));
      PetscCall(ISLocalToGlobalMappingCreateIS(Pg, &l2gmap_p));
      PetscCall(ISDestroy(&Pg));
      PetscCall(PetscLayoutCreate(comm, &play));
      PetscCall(PetscLayoutSetBlockSize(play, 1));
      PetscCall(PetscLayoutSetSize(play, nPg));
      PetscCall(ISGetLocalSize(pP, &nPgl));
      PetscCall(PetscLayoutSetLocalSize(play, nPgl));
      PetscCall(PetscLayoutSetUp(play));
    } else {
      PetscCall(PetscObjectReference((PetscObject)fetidpmat_ctx->C));
      PetscCall(MatISGetLocalToGlobalMapping(fetidpmat_ctx->C, &l2gmap_p, NULL));
      PetscCall(PetscObjectReference((PetscObject)l2gmap_p));
      PetscCall(MatGetSize(fetidpmat_ctx->C, &nPg, NULL));
      PetscCall(MatGetLocalSize(fetidpmat_ctx->C, NULL, &nPgl));
      PetscCall(MatGetLayouts(fetidpmat_ctx->C, NULL, &llay));
      PetscCall(PetscLayoutReference(llay, &play));
    }
    PetscCall(VecCreateMPIWithArray(comm, 1, nPgl, nPg, NULL, &fetidpmat_ctx->xPg));
    PetscCall(VecCreateMPIWithArray(comm, 1, nPgl, nPg, NULL, &fetidpmat_ctx->yPg));

    /* import matrices for pressures coupling */
    PetscCall(PetscObjectQuery((PetscObject)fetidpmat_ctx->pc, "__KSPFETIDP_B_BI", (PetscObject *)&fetidpmat_ctx->B_BI));
    PetscCheck(fetidpmat_ctx->B_BI, PETSC_COMM_SELF, PETSC_ERR_PLIB, "B_BI not present");
    PetscCall(PetscObjectReference((PetscObject)fetidpmat_ctx->B_BI));

    PetscCall(PetscObjectQuery((PetscObject)fetidpmat_ctx->pc, "__KSPFETIDP_B_BB", (PetscObject *)&fetidpmat_ctx->B_BB));
    PetscCheck(fetidpmat_ctx->B_BB, PETSC_COMM_SELF, PETSC_ERR_PLIB, "B_BB not present");
    PetscCall(PetscObjectReference((PetscObject)fetidpmat_ctx->B_BB));

    PetscCall(PetscObjectQuery((PetscObject)fetidpmat_ctx->pc, "__KSPFETIDP_Bt_BI", (PetscObject *)&fetidpmat_ctx->Bt_BI));
    PetscCheck(fetidpmat_ctx->Bt_BI, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Bt_BI not present");
    PetscCall(PetscObjectReference((PetscObject)fetidpmat_ctx->Bt_BI));

    PetscCall(PetscObjectQuery((PetscObject)fetidpmat_ctx->pc, "__KSPFETIDP_Bt_BB", (PetscObject *)&fetidpmat_ctx->Bt_BB));
    PetscCheck(fetidpmat_ctx->Bt_BB, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Bt_BB not present");
    PetscCall(PetscObjectReference((PetscObject)fetidpmat_ctx->Bt_BB));

    PetscCall(PetscObjectQuery((PetscObject)fetidpmat_ctx->pc, "__KSPFETIDP_flip", (PetscObject *)&fetidpmat_ctx->rhs_flip));
    if (fetidpmat_ctx->rhs_flip) PetscCall(PetscObjectReference((PetscObject)fetidpmat_ctx->rhs_flip));

    PetscCall(PetscObjectQuery((PetscObject)fetidpmat_ctx->pc, "__KSPFETIDP_lP_I", (PetscObject *)&fetidpmat_ctx->lP_I));
    PetscCheck(fetidpmat_ctx->lP_I, PETSC_COMM_SELF, PETSC_ERR_PLIB, "lP_I not present");
    PetscCall(PetscObjectReference((PetscObject)fetidpmat_ctx->lP_I));

    PetscCall(PetscObjectQuery((PetscObject)fetidpmat_ctx->pc, "__KSPFETIDP_lP_B", (PetscObject *)&fetidpmat_ctx->lP_B));
    PetscCheck(fetidpmat_ctx->lP_B, PETSC_COMM_SELF, PETSC_ERR_PLIB, "lP_B not present");
    PetscCall(PetscObjectReference((PetscObject)fetidpmat_ctx->lP_B));
  }

  /* Default type of lagrange multipliers is non-redundant */
  fully_redundant = fetidpmat_ctx->fully_redundant;

  /* Evaluate local and global number of lagrange multipliers */
  PetscCall(VecSet(pcis->vec1_N, 0.0));
  n_local_lambda  = 0;
  partial_sum     = 0;
  n_boundary_dofs = 0;

  /* Get Vertices used to define the BDDC */
  PetscCall(PCBDDCGraphGetCandidatesIS(mat_graph, NULL, NULL, NULL, NULL, &isvert));
  PetscCall(ISGetLocalSize(isvert, &n_vertices));
  PetscCall(ISGetIndices(isvert, &vertex_indices));

  dual_size = pcis->n_B - n_vertices;
  PetscCall(PetscMalloc1(dual_size, &dual_dofs_boundary_indices));
  PetscCall(PetscMalloc1(dual_size, &aux_local_numbering_1));
  PetscCall(PetscMalloc1(dual_size, &aux_local_numbering_2));

  /* the code below does not support multiple subdomains per process
     error out in this case
     TODO: I guess I can use PetscSFGetMultiSF and the code will be easier and more general */
  PetscCall(PetscMalloc2(pcis->n, &count, pcis->n, &neighbours_set));
  for (i = 0, j = 0; i < pcis->n; i++) j += mat_graph->nodes[i].count;
  if (pcis->n) PetscCall(PetscMalloc1(j, &neighbours_set[0]));
  for (i = 0; i < pcis->n; i++) {
    PCBDDCGraphNode *node = &mat_graph->nodes[i];

    count[i] = 0;
    for (j = 0; j < node->count; j++) {
      if (node->neighbours_set[j] == rank) continue;
      neighbours_set[i][count[i]++] = node->neighbours_set[j];
    }
    PetscCheck(count[i] == node->count - 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "Multiple subdomains per process not supported");
    s = count[i];
    PetscCall(PetscSortRemoveDupsInt(count + i, neighbours_set[i]));
    PetscCheck(s == count[i], PETSC_COMM_SELF, PETSC_ERR_SUP, "Multiple subdomains per process not supported");
    if (i != pcis->n - 1) neighbours_set[i + 1] = neighbours_set[i] + count[i];
  }

  PetscCall(VecGetArray(pcis->vec1_N, &array));
  for (i = 0, s = 0; i < pcis->n; i++) {
    j = count[i]; /* RECALL: count[i] does not count myself */
    if (j > 0) n_boundary_dofs++;
    skip_node = PETSC_FALSE;
    if (s < n_vertices && vertex_indices[s] == i) { /* it works for a sorted set of vertices */
      skip_node = PETSC_TRUE;
      s++;
    }
    if (j < 1) skip_node = PETSC_TRUE;
    if (mat_graph->nodes[i].special_dof == PCBDDCGRAPH_DIRICHLET_MARK) skip_node = PETSC_TRUE;
    if (!skip_node) {
      if (fully_redundant) {
        /* fully redundant set of lagrange multipliers */
        n_lambda_for_dof = (j * (j + 1)) / 2;
      } else {
        n_lambda_for_dof = j;
      }
      n_local_lambda += j;
      /* needed to evaluate global number of lagrange multipliers */
      array[i] = (1.0 * n_lambda_for_dof) / (j + 1.0); /* already scaled for the next global sum */
      /* store some data needed */
      dual_dofs_boundary_indices[partial_sum] = n_boundary_dofs - 1;
      aux_local_numbering_1[partial_sum]      = i;
      aux_local_numbering_2[partial_sum]      = n_lambda_for_dof;
      partial_sum++;
    }
  }
  PetscCall(VecRestoreArray(pcis->vec1_N, &array));
  PetscCall(ISRestoreIndices(isvert, &vertex_indices));
  PetscCall(PCBDDCGraphRestoreCandidatesIS(mat_graph, NULL, NULL, NULL, NULL, &isvert));
  dual_size = partial_sum;

  /* compute global ordering of lagrange multipliers and associate l2g map */
  PetscCall(ISCreateGeneral(comm, partial_sum, aux_local_numbering_1, PETSC_COPY_VALUES, &subset_n));
  PetscCall(ISLocalToGlobalMappingApplyIS(pcis->mapping, subset_n, &subset));
  PetscCall(ISDestroy(&subset_n));
  PetscCall(ISCreateGeneral(comm, partial_sum, aux_local_numbering_2, PETSC_OWN_POINTER, &subset_mult));
  PetscCall(ISRenumber(subset, subset_mult, &fetidpmat_ctx->n_lambda, &subset_n));
  PetscCall(ISDestroy(&subset));

  if (PetscDefined(USE_DEBUG)) {
    PetscCall(VecSet(pcis->vec1_global, 0.0));
    PetscCall(VecScatterBegin(matis->rctx, pcis->vec1_N, pcis->vec1_global, ADD_VALUES, SCATTER_REVERSE));
    PetscCall(VecScatterEnd(matis->rctx, pcis->vec1_N, pcis->vec1_global, ADD_VALUES, SCATTER_REVERSE));
    PetscCall(VecSum(pcis->vec1_global, &scalar_value));
    i = (PetscInt)PetscRealPart(scalar_value);
    PetscCheck(i == fetidpmat_ctx->n_lambda, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "Global number of multipliers mismatch! (%" PetscInt_FMT " != %" PetscInt_FMT ")", fetidpmat_ctx->n_lambda, i);
  }

  /* init data for scaling factors exchange */
  if (!pcbddc->use_deluxe_scaling) {
    PetscInt    *ptrs_buffer, neigh_position;
    PetscScalar *send_buffer, *recv_buffer;
    MPI_Request *send_reqs, *recv_reqs;
    PetscMPIInt  nreqs;

    partial_sum = 0;
    PetscCall(PetscMalloc1(pcis->n_neigh, &ptrs_buffer));
    PetscCall(PetscMalloc1(PetscMax(pcis->n_neigh - 1, 0), &send_reqs));
    PetscCall(PetscMalloc1(PetscMax(pcis->n_neigh - 1, 0), &recv_reqs));
    PetscCall(PetscMalloc1(pcis->n + 1, &all_factors));
    if (pcis->n_neigh > 0) ptrs_buffer[0] = 0;
    for (i = 1; i < pcis->n_neigh; i++) {
      partial_sum += pcis->n_shared[i];
      ptrs_buffer[i] = ptrs_buffer[i - 1] + pcis->n_shared[i];
    }
    PetscCall(PetscMalloc1(partial_sum, &send_buffer));
    PetscCall(PetscMalloc1(partial_sum, &recv_buffer));
    PetscCall(PetscMalloc1(partial_sum, &all_factors[0]));
    for (i = 0; i < pcis->n - 1; i++) {
      j                  = count[i];
      all_factors[i + 1] = all_factors[i] + j;
    }

    /* scatter B scaling to N vec */
    PetscCall(VecScatterBegin(pcis->N_to_B, pcis->D, pcis->vec1_N, INSERT_VALUES, SCATTER_REVERSE));
    PetscCall(VecScatterEnd(pcis->N_to_B, pcis->D, pcis->vec1_N, INSERT_VALUES, SCATTER_REVERSE));
    /* communications */
    PetscCall(VecGetArrayRead(pcis->vec1_N, (const PetscScalar **)&array));
    for (i = 1; i < pcis->n_neigh; i++) {
      for (j = 0; j < pcis->n_shared[i]; j++) send_buffer[ptrs_buffer[i - 1] + j] = array[pcis->shared[i][j]];
      buf_size = ptrs_buffer[i] - ptrs_buffer[i - 1];
      PetscCall(PetscMPIIntCast(pcis->neigh[i], &neigh));
      PetscCallMPI(MPIU_Isend(&send_buffer[ptrs_buffer[i - 1]], buf_size, MPIU_SCALAR, neigh, 0, comm, &send_reqs[i - 1]));
      PetscCallMPI(MPIU_Irecv(&recv_buffer[ptrs_buffer[i - 1]], buf_size, MPIU_SCALAR, neigh, 0, comm, &recv_reqs[i - 1]));
    }
    PetscCall(VecRestoreArrayRead(pcis->vec1_N, (const PetscScalar **)&array));
    PetscCall(PetscMPIIntCast(pcis->n_neigh - 1, &nreqs));
    if (pcis->n_neigh > 0) PetscCallMPI(MPI_Waitall(nreqs, recv_reqs, MPI_STATUSES_IGNORE));
    /* put values in correct places */
    for (i = 1; i < pcis->n_neigh; i++) {
      for (j = 0; j < pcis->n_shared[i]; j++) {
        k              = pcis->shared[i][j];
        neigh_position = 0;
        while (neighbours_set[k][neigh_position] != pcis->neigh[i]) neigh_position++;
        all_factors[k][neigh_position] = recv_buffer[ptrs_buffer[i - 1] + j];
      }
    }
    if (pcis->n_neigh > 0) PetscCallMPI(MPI_Waitall(nreqs, send_reqs, MPI_STATUSES_IGNORE));
    PetscCall(PetscFree(send_reqs));
    PetscCall(PetscFree(recv_reqs));
    PetscCall(PetscFree(send_buffer));
    PetscCall(PetscFree(recv_buffer));
    PetscCall(PetscFree(ptrs_buffer));
  }

  /* Compute B and B_delta (local actions) */
  PetscCall(PetscMalloc1(pcis->n_neigh, &aux_sums));
  PetscCall(PetscMalloc1(n_local_lambda, &l2g_indices));
  PetscCall(PetscMalloc1(n_local_lambda, &vals_B_delta));
  PetscCall(PetscMalloc1(n_local_lambda, &cols_B_delta));
  if (!pcbddc->use_deluxe_scaling) {
    PetscCall(PetscMalloc1(n_local_lambda, &scaling_factors));
  } else {
    scaling_factors = NULL;
    all_factors     = NULL;
  }
  PetscCall(ISGetIndices(subset_n, &aux_global_numbering));
  partial_sum = 0;
  cum         = 0;
  for (i = 0; i < dual_size; i++) {
    n_global_lambda = aux_global_numbering[cum];
    j               = count[aux_local_numbering_1[i]];
    aux_sums[0]     = 0;
    for (s = 1; s < j; s++) aux_sums[s] = aux_sums[s - 1] + j - s + 1;
    if (all_factors) array = all_factors[aux_local_numbering_1[i]];
    n_neg_values = 0;
    while (n_neg_values < j && neighbours_set[aux_local_numbering_1[i]][n_neg_values] < rank) n_neg_values++;
    n_pos_values = j - n_neg_values;
    if (fully_redundant) {
      for (s = 0; s < n_neg_values; s++) {
        l2g_indices[partial_sum + s]  = aux_sums[s] + n_neg_values - s - 1 + n_global_lambda;
        cols_B_delta[partial_sum + s] = dual_dofs_boundary_indices[i];
        vals_B_delta[partial_sum + s] = -1.0;
        if (!pcbddc->use_deluxe_scaling) scaling_factors[partial_sum + s] = array[s];
      }
      for (s = 0; s < n_pos_values; s++) {
        l2g_indices[partial_sum + s + n_neg_values]  = aux_sums[n_neg_values] + s + n_global_lambda;
        cols_B_delta[partial_sum + s + n_neg_values] = dual_dofs_boundary_indices[i];
        vals_B_delta[partial_sum + s + n_neg_values] = 1.0;
        if (!pcbddc->use_deluxe_scaling) scaling_factors[partial_sum + s + n_neg_values] = array[s + n_neg_values];
      }
      partial_sum += j;
    } else {
      /* l2g_indices and default cols and vals of B_delta */
      for (s = 0; s < j; s++) {
        l2g_indices[partial_sum + s]  = n_global_lambda + s;
        cols_B_delta[partial_sum + s] = dual_dofs_boundary_indices[i];
        vals_B_delta[partial_sum + s] = 0.0;
      }
      /* B_delta */
      if (n_neg_values > 0) { /* there's a rank next to me to the left */
        vals_B_delta[partial_sum + n_neg_values - 1] = -1.0;
      }
      if (n_neg_values < j) { /* there's a rank next to me to the right */
        vals_B_delta[partial_sum + n_neg_values] = 1.0;
      }
      /* scaling as in Klawonn-Widlund 1999 */
      if (!pcbddc->use_deluxe_scaling) {
        for (s = 0; s < n_neg_values; s++) {
          scalar_value = 0.0;
          for (k = 0; k < s + 1; k++) scalar_value += array[k];
          scaling_factors[partial_sum + s] = -scalar_value;
        }
        for (s = 0; s < n_pos_values; s++) {
          scalar_value = 0.0;
          for (k = s + n_neg_values; k < j; k++) scalar_value += array[k];
          scaling_factors[partial_sum + s + n_neg_values] = scalar_value;
        }
      }
      partial_sum += j;
    }
    cum += aux_local_numbering_2[i];
  }
  PetscCall(ISRestoreIndices(subset_n, &aux_global_numbering));
  PetscCall(ISDestroy(&subset_mult));
  PetscCall(ISDestroy(&subset_n));
  PetscCall(PetscFree(aux_sums));
  PetscCall(PetscFree(aux_local_numbering_1));
  PetscCall(PetscFree(dual_dofs_boundary_indices));
  if (all_factors) {
    PetscCall(PetscFree(all_factors[0]));
    PetscCall(PetscFree(all_factors));
  }
  if (pcis->n) PetscCall(PetscFree(neighbours_set[0]));
  PetscCall(PetscFree2(count, neighbours_set));

  /* Create local part of B_delta */
  PetscCall(MatCreate(PETSC_COMM_SELF, &fetidpmat_ctx->B_delta));
  PetscCall(MatSetSizes(fetidpmat_ctx->B_delta, n_local_lambda, pcis->n_B, n_local_lambda, pcis->n_B));
  PetscCall(MatSetType(fetidpmat_ctx->B_delta, MATSEQAIJ));
  PetscCall(MatSeqAIJSetPreallocation(fetidpmat_ctx->B_delta, 1, NULL));
  PetscCall(MatSetOption(fetidpmat_ctx->B_delta, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE));
  for (i = 0; i < n_local_lambda; i++) PetscCall(MatSetValue(fetidpmat_ctx->B_delta, i, cols_B_delta[i], vals_B_delta[i], INSERT_VALUES));
  PetscCall(PetscFree(vals_B_delta));
  PetscCall(MatAssemblyBegin(fetidpmat_ctx->B_delta, MAT_FINAL_ASSEMBLY));
  PetscCall(MatAssemblyEnd(fetidpmat_ctx->B_delta, MAT_FINAL_ASSEMBLY));

  BD1 = NULL;
  BD2 = NULL;
  if (fully_redundant) {
    PetscCheck(!pcbddc->use_deluxe_scaling, comm, PETSC_ERR_SUP, "Deluxe FETIDP with fully-redundant multipliers to be implemented");
    PetscCall(MatCreate(PETSC_COMM_SELF, &ScalingMat));
    PetscCall(MatSetSizes(ScalingMat, n_local_lambda, n_local_lambda, n_local_lambda, n_local_lambda));
    PetscCall(MatSetType(ScalingMat, MATSEQAIJ));
    PetscCall(MatSeqAIJSetPreallocation(ScalingMat, 1, NULL));
    for (i = 0; i < n_local_lambda; i++) PetscCall(MatSetValue(ScalingMat, i, i, scaling_factors[i], INSERT_VALUES));
    PetscCall(MatAssemblyBegin(ScalingMat, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(ScalingMat, MAT_FINAL_ASSEMBLY));
    PetscCall(MatMatMult(ScalingMat, fetidpmat_ctx->B_delta, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &fetidpmat_ctx->B_Ddelta));
    PetscCall(MatDestroy(&ScalingMat));
  } else {
    PetscCall(MatCreate(PETSC_COMM_SELF, &fetidpmat_ctx->B_Ddelta));
    PetscCall(MatSetSizes(fetidpmat_ctx->B_Ddelta, n_local_lambda, pcis->n_B, n_local_lambda, pcis->n_B));
    if (!pcbddc->use_deluxe_scaling || !pcbddc->sub_schurs) {
      PetscCall(MatSetType(fetidpmat_ctx->B_Ddelta, MATSEQAIJ));
      PetscCall(MatSeqAIJSetPreallocation(fetidpmat_ctx->B_Ddelta, 1, NULL));
      for (i = 0; i < n_local_lambda; i++) PetscCall(MatSetValue(fetidpmat_ctx->B_Ddelta, i, cols_B_delta[i], scaling_factors[i], INSERT_VALUES));
      PetscCall(MatAssemblyBegin(fetidpmat_ctx->B_Ddelta, MAT_FINAL_ASSEMBLY));
      PetscCall(MatAssemblyEnd(fetidpmat_ctx->B_Ddelta, MAT_FINAL_ASSEMBLY));
    } else {
      /* scaling as in Klawonn-Widlund 1999 */
      PCBDDCDeluxeScaling deluxe_ctx = pcbddc->deluxe_ctx;
      PCBDDCSubSchurs     sub_schurs = pcbddc->sub_schurs;
      Mat                 T;
      PetscScalar        *W, lwork, *Bwork;
      const PetscInt     *idxs = NULL;
      PetscInt            cum, mss, *nnz;
      PetscBLASInt       *pivots, B_lwork, B_N, B_ierr;

      PetscCheck(pcbddc->deluxe_singlemat, comm, PETSC_ERR_USER, "Cannot compute B_Ddelta! rerun with -pc_bddc_deluxe_singlemat");
      mss = 0;
      PetscCall(PetscCalloc1(pcis->n_B, &nnz));
      if (sub_schurs->is_Ej_all) {
        PetscCall(ISGetIndices(sub_schurs->is_Ej_all, &idxs));
        for (i = 0, cum = 0; i < sub_schurs->n_subs; i++) {
          PetscInt subset_size;

          PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
          for (j = 0; j < subset_size; j++) nnz[idxs[j + cum]] = subset_size;
          mss = PetscMax(mss, subset_size);
          cum += subset_size;
        }
      }
      PetscCall(MatCreate(PETSC_COMM_SELF, &T));
      PetscCall(MatSetSizes(T, pcis->n_B, pcis->n_B, pcis->n_B, pcis->n_B));
      PetscCall(MatSetType(T, MATSEQAIJ));
      PetscCall(MatSeqAIJSetPreallocation(T, 0, nnz));
      PetscCall(PetscFree(nnz));

      /* workspace allocation */
      B_lwork = 0;
      if (mss) {
        PetscScalar dummy = 1;

        B_lwork = -1;
        PetscCall(PetscBLASIntCast(mss, &B_N));
        PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
        PetscCallBLAS("LAPACKgetri", LAPACKgetri_(&B_N, &dummy, &B_N, &B_N, &lwork, &B_lwork, &B_ierr));
        PetscCall(PetscFPTrapPop());
        PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in query to GETRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
        PetscCall(PetscBLASIntCast((PetscInt)PetscRealPart(lwork), &B_lwork));
      }
      PetscCall(PetscMalloc3(mss * mss, &W, mss, &pivots, B_lwork, &Bwork));

      for (i = 0, cum = 0; i < sub_schurs->n_subs; i++) {
        const PetscScalar *M;
        PetscInt           subset_size;

        PetscCall(ISGetLocalSize(sub_schurs->is_subs[i], &subset_size));
        PetscCall(PetscBLASIntCast(subset_size, &B_N));
        PetscCall(MatDenseGetArrayRead(deluxe_ctx->seq_mat[i], &M));
        PetscCall(PetscArraycpy(W, M, subset_size * subset_size));
        PetscCall(MatDenseRestoreArrayRead(deluxe_ctx->seq_mat[i], &M));
        PetscCall(PetscFPTrapPush(PETSC_FP_TRAP_OFF));
        PetscCallBLAS("LAPACKgetrf", LAPACKgetrf_(&B_N, &B_N, W, &B_N, pivots, &B_ierr));
        PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GETRF Lapack routine %" PetscBLASInt_FMT, B_ierr);
        PetscCallBLAS("LAPACKgetri", LAPACKgetri_(&B_N, W, &B_N, pivots, Bwork, &B_lwork, &B_ierr));
        PetscCheck(!B_ierr, PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in GETRI Lapack routine %" PetscBLASInt_FMT, B_ierr);
        PetscCall(PetscFPTrapPop());
        /* silent static analyzer */
        PetscCheck(idxs, PETSC_COMM_SELF, PETSC_ERR_PLIB, "IDXS not present");
        PetscCall(MatSetValues(T, subset_size, idxs + cum, subset_size, idxs + cum, W, INSERT_VALUES));
        cum += subset_size;
      }
      PetscCall(MatAssemblyBegin(T, MAT_FINAL_ASSEMBLY));
      PetscCall(MatAssemblyEnd(T, MAT_FINAL_ASSEMBLY));
      PetscCall(MatMatTransposeMult(T, fetidpmat_ctx->B_delta, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &BD1));
      PetscCall(MatMatMult(fetidpmat_ctx->B_delta, BD1, MAT_INITIAL_MATRIX, PETSC_DETERMINE, &BD2));
      PetscCall(MatDestroy(&T));
      PetscCall(PetscFree3(W, pivots, Bwork));
      if (sub_schurs->is_Ej_all) PetscCall(ISRestoreIndices(sub_schurs->is_Ej_all, &idxs));
    }
  }
  PetscCall(PetscFree(scaling_factors));
  PetscCall(PetscFree(cols_B_delta));

  /* Layout of multipliers */
  PetscCall(PetscLayoutCreate(comm, &llay));
  PetscCall(PetscLayoutSetBlockSize(llay, 1));
  PetscCall(PetscLayoutSetSize(llay, fetidpmat_ctx->n_lambda));
  PetscCall(PetscLayoutSetUp(llay));
  PetscCall(PetscLayoutGetLocalSize(llay, &fetidpmat_ctx->n));

  /* Local work vector of multipliers */
  PetscCall(VecCreate(PETSC_COMM_SELF, &fetidpmat_ctx->lambda_local));
  PetscCall(VecSetSizes(fetidpmat_ctx->lambda_local, n_local_lambda, n_local_lambda));
  PetscCall(VecSetType(fetidpmat_ctx->lambda_local, VECSEQ));

  if (BD2) {
    ISLocalToGlobalMapping l2g;
    Mat                    T, TA, *pT;
    IS                     is;
    PetscInt               nl, N;
    BDdelta_DN             ctx;

    PetscCall(PetscLayoutGetLocalSize(llay, &nl));
    PetscCall(PetscLayoutGetSize(llay, &N));
    PetscCall(MatCreate(comm, &T));
    PetscCall(MatSetSizes(T, nl, nl, N, N));
    PetscCall(MatSetType(T, MATIS));
    PetscCall(ISLocalToGlobalMappingCreate(comm, 1, n_local_lambda, l2g_indices, PETSC_COPY_VALUES, &l2g));
    PetscCall(MatSetLocalToGlobalMapping(T, l2g, l2g));
    PetscCall(ISLocalToGlobalMappingDestroy(&l2g));
    PetscCall(MatISSetLocalMat(T, BD2));
    PetscCall(MatAssemblyBegin(T, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(T, MAT_FINAL_ASSEMBLY));
    PetscCall(MatDestroy(&BD2));
    PetscCall(MatConvert(T, MATAIJ, MAT_INITIAL_MATRIX, &TA));
    PetscCall(MatDestroy(&T));
    PetscCall(ISCreateGeneral(comm, n_local_lambda, l2g_indices, PETSC_USE_POINTER, &is));
    PetscCall(MatCreateSubMatrices(TA, 1, &is, &is, MAT_INITIAL_MATRIX, &pT));
    PetscCall(MatDestroy(&TA));
    PetscCall(ISDestroy(&is));
    BD2 = pT[0];
    PetscCall(PetscFree(pT));

    /* B_Ddelta for non-redundant multipliers with deluxe scaling */
    PetscCall(PetscNew(&ctx));
    PetscCall(MatSetType(fetidpmat_ctx->B_Ddelta, MATSHELL));
    PetscCall(MatShellSetContext(fetidpmat_ctx->B_Ddelta, ctx));
    PetscCall(MatShellSetOperation(fetidpmat_ctx->B_Ddelta, MATOP_MULT, (PetscErrorCodeFn *)MatMult_BDdelta_deluxe_nonred));
    PetscCall(MatShellSetOperation(fetidpmat_ctx->B_Ddelta, MATOP_MULT_TRANSPOSE, (PetscErrorCodeFn *)MatMultTranspose_BDdelta_deluxe_nonred));
    PetscCall(MatShellSetOperation(fetidpmat_ctx->B_Ddelta, MATOP_DESTROY, (PetscErrorCodeFn *)MatDestroy_BDdelta_deluxe_nonred));
    PetscCall(MatSetUp(fetidpmat_ctx->B_Ddelta));

    PetscCall(PetscObjectReference((PetscObject)BD1));
    ctx->BD = BD1;
    PetscCall(KSPCreate(PETSC_COMM_SELF, &ctx->kBD));
    PetscCall(KSPSetNestLevel(ctx->kBD, fetidpmat_ctx->pc->kspnestlevel));
    PetscCall(KSPSetOperators(ctx->kBD, BD2, BD2));
    PetscCall(VecDuplicate(fetidpmat_ctx->lambda_local, &ctx->work));
    fetidpmat_ctx->deluxe_nonred = PETSC_TRUE;
  }
  PetscCall(MatDestroy(&BD1));
  PetscCall(MatDestroy(&BD2));

  /* fetidpmat sizes */
  fetidpmat_ctx->n += nPgl;
  fetidpmat_ctx->N = fetidpmat_ctx->n_lambda + nPg;

  /* Global vector for FETI-DP linear system */
  PetscCall(VecCreate(comm, &fetidp_global));
  PetscCall(VecSetSizes(fetidp_global, fetidpmat_ctx->n, fetidpmat_ctx->N));
  PetscCall(VecSetType(fetidp_global, VECMPI));
  PetscCall(VecSetUp(fetidp_global));

  /* Decide layout for fetidp dofs: if it is a saddle point problem
     pressure is ordered first in the local part of the global vector
     of the FETI-DP linear system */
  if (nPg) {
    Vec             v;
    IS              IS_l2g_p, ais;
    PetscLayout     alay;
    const PetscInt *idxs, *pranges, *aranges, *lranges;
    PetscInt       *l2g_indices_p, rst;
    PetscMPIInt     rank;

    PetscCall(PetscMalloc1(nPl, &l2g_indices_p));
    PetscCall(VecGetLayout(fetidp_global, &alay));
    PetscCall(PetscLayoutGetRanges(alay, &aranges));
    PetscCall(PetscLayoutGetRanges(play, &pranges));
    PetscCall(PetscLayoutGetRanges(llay, &lranges));

    PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)fetidp_global), &rank));
    PetscCall(ISCreateStride(PetscObjectComm((PetscObject)fetidp_global), pranges[rank + 1] - pranges[rank], aranges[rank], 1, &fetidpmat_ctx->pressure));
    PetscCall(PetscObjectSetName((PetscObject)fetidpmat_ctx->pressure, "F_P"));
    PetscCall(ISCreateStride(PetscObjectComm((PetscObject)fetidp_global), lranges[rank + 1] - lranges[rank], aranges[rank] + pranges[rank + 1] - pranges[rank], 1, &fetidpmat_ctx->lagrange));
    PetscCall(PetscObjectSetName((PetscObject)fetidpmat_ctx->lagrange, "F_L"));
    PetscCall(ISLocalToGlobalMappingGetIndices(l2gmap_p, &idxs));
    /* shift local to global indices for pressure */
    for (i = 0; i < nPl; i++) {
      PetscMPIInt owner;

      PetscCall(PetscLayoutFindOwner(play, idxs[i], &owner));
      l2g_indices_p[i] = idxs[i] - pranges[owner] + aranges[owner];
    }
    PetscCall(ISLocalToGlobalMappingRestoreIndices(l2gmap_p, &idxs));
    PetscCall(ISCreateGeneral(comm, nPl, l2g_indices_p, PETSC_OWN_POINTER, &IS_l2g_p));

    /* local to global scatter for pressure */
    PetscCall(VecScatterCreate(fetidpmat_ctx->vP, NULL, fetidp_global, IS_l2g_p, &fetidpmat_ctx->l2g_p));
    PetscCall(ISDestroy(&IS_l2g_p));

    /* scatter for lagrange multipliers only */
    PetscCall(VecCreate(comm, &v));
    PetscCall(VecSetType(v, VECSTANDARD));
    PetscCall(VecSetLayout(v, llay));
    PetscCall(VecSetUp(v));
    PetscCall(ISCreateGeneral(comm, n_local_lambda, l2g_indices, PETSC_COPY_VALUES, &ais));
    PetscCall(VecScatterCreate(fetidpmat_ctx->lambda_local, NULL, v, ais, &fetidpmat_ctx->l2g_lambda_only));
    PetscCall(ISDestroy(&ais));
    PetscCall(VecDestroy(&v));

    /* shift local to global indices for multipliers */
    for (i = 0; i < n_local_lambda; i++) {
      PetscInt    ps;
      PetscMPIInt owner;

      PetscCall(PetscLayoutFindOwner(llay, l2g_indices[i], &owner));
      ps             = pranges[owner + 1] - pranges[owner];
      l2g_indices[i] = l2g_indices[i] - lranges[owner] + aranges[owner] + ps;
    }

    /* scatter from alldofs to pressures global fetidp vector */
    PetscCall(PetscLayoutGetRange(alay, &rst, NULL));
    PetscCall(ISCreateStride(comm, nPgl, rst, 1, &ais));
    PetscCall(VecScatterCreate(pcis->vec1_global, pP, fetidp_global, ais, &fetidpmat_ctx->g2g_p));
    PetscCall(ISDestroy(&ais));
  }
  PetscCall(PetscLayoutDestroy(&llay));
  PetscCall(PetscLayoutDestroy(&play));
  PetscCall(ISCreateGeneral(comm, n_local_lambda, l2g_indices, PETSC_OWN_POINTER, &IS_l2g_lambda));

  /* scatter from local to global multipliers */
  PetscCall(VecScatterCreate(fetidpmat_ctx->lambda_local, NULL, fetidp_global, IS_l2g_lambda, &fetidpmat_ctx->l2g_lambda));
  PetscCall(ISDestroy(&IS_l2g_lambda));
  PetscCall(ISLocalToGlobalMappingDestroy(&l2gmap_p));
  PetscCall(VecDestroy(&fetidp_global));

  /* Create some work vectors needed by fetidp */
  PetscCall(VecDuplicate(pcis->vec1_B, &fetidpmat_ctx->temp_solution_B));
  PetscCall(VecDuplicate(pcis->vec1_D, &fetidpmat_ctx->temp_solution_D));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PCBDDCSetupFETIDPPCContext(Mat fetimat, FETIDPPC_ctx fetidppc_ctx)
{
  FETIDPMat_ctx mat_ctx;
  PC_BDDC      *pcbddc = (PC_BDDC *)fetidppc_ctx->pc->data;
  PC_IS        *pcis   = (PC_IS *)fetidppc_ctx->pc->data;
  PetscBool     lumped = PETSC_FALSE;

  PetscFunctionBegin;
  PetscCall(MatShellGetContext(fetimat, &mat_ctx));
  /* get references from objects created when setting up feti mat context */
  PetscCall(PetscObjectReference((PetscObject)mat_ctx->lambda_local));
  fetidppc_ctx->lambda_local = mat_ctx->lambda_local;
  PetscCall(PetscObjectReference((PetscObject)mat_ctx->B_Ddelta));
  fetidppc_ctx->B_Ddelta = mat_ctx->B_Ddelta;
  if (mat_ctx->deluxe_nonred) {
    PC            pc, mpc;
    BDdelta_DN    ctx;
    MatSolverType solver;
    const char   *prefix;

    PetscCall(MatShellGetContext(mat_ctx->B_Ddelta, &ctx));
    PetscCall(KSPSetType(ctx->kBD, KSPPREONLY));
    PetscCall(KSPGetPC(ctx->kBD, &mpc));
    PetscCall(KSPGetPC(pcbddc->ksp_D, &pc));
    PetscCall(PCSetType(mpc, PCLU));
    PetscCall(PCFactorGetMatSolverType(pc, &solver));
    if (solver) PetscCall(PCFactorSetMatSolverType(mpc, solver));
    PetscCall(MatGetOptionsPrefix(fetimat, &prefix));
    PetscCall(KSPSetOptionsPrefix(ctx->kBD, prefix));
    PetscCall(KSPAppendOptionsPrefix(ctx->kBD, "bddelta_"));
    PetscCall(KSPSetFromOptions(ctx->kBD));
  }

  if (mat_ctx->l2g_lambda_only) {
    PetscCall(PetscObjectReference((PetscObject)mat_ctx->l2g_lambda_only));
    fetidppc_ctx->l2g_lambda = mat_ctx->l2g_lambda_only;
  } else {
    PetscCall(PetscObjectReference((PetscObject)mat_ctx->l2g_lambda));
    fetidppc_ctx->l2g_lambda = mat_ctx->l2g_lambda;
  }
  /* Dirichlet preconditioner */
  PetscCall(PetscOptionsGetBool(NULL, ((PetscObject)fetimat)->prefix, "-pc_lumped", &lumped, NULL));
  if (!lumped) {
    IS        iV;
    PetscBool discrete_harmonic = PETSC_FALSE;

    PetscCall(PetscObjectQuery((PetscObject)fetidppc_ctx->pc, "__KSPFETIDP_iV", (PetscObject *)&iV));
    if (iV) PetscCall(PetscOptionsGetBool(NULL, ((PetscObject)fetimat)->prefix, "-pc_discrete_harmonic", &discrete_harmonic, NULL));
    if (discrete_harmonic) {
      KSP             sksp;
      PC              pc;
      PCBDDCSubSchurs sub_schurs = pcbddc->sub_schurs;
      Mat             A_II, A_IB, A_BI;
      IS              iP = NULL;
      PetscBool       isshell, reuse = PETSC_FALSE;
      KSPType         ksptype;
      const char     *prefix;

      /*
        We constructs a Schur complement for

        | A_II A_ID |
        | A_DI A_DD |

        instead of

        | A_II  B^t_II A_ID |
        | B_II -C_II   B_ID |
        | A_DI  B^t_ID A_DD |

      */
      if (sub_schurs && sub_schurs->reuse_solver) {
        PetscCall(PetscObjectQuery((PetscObject)sub_schurs->A, "__KSPFETIDP_iP", (PetscObject *)&iP));
        if (iP) reuse = PETSC_TRUE;
      }
      if (!reuse) {
        IS       aB;
        PetscInt nb;
        PetscCall(ISGetLocalSize(pcis->is_B_local, &nb));
        PetscCall(ISCreateStride(PetscObjectComm((PetscObject)pcis->A_II), nb, 0, 1, &aB));
        PetscCall(MatCreateSubMatrix(pcis->A_II, iV, iV, MAT_INITIAL_MATRIX, &A_II));
        PetscCall(MatCreateSubMatrix(pcis->A_IB, iV, aB, MAT_INITIAL_MATRIX, &A_IB));
        PetscCall(MatCreateSubMatrix(pcis->A_BI, aB, iV, MAT_INITIAL_MATRIX, &A_BI));
        PetscCall(ISDestroy(&aB));
      } else {
        PetscCall(MatCreateSubMatrix(sub_schurs->A, pcis->is_I_local, pcis->is_B_local, MAT_INITIAL_MATRIX, &A_IB));
        PetscCall(MatCreateSubMatrix(sub_schurs->A, pcis->is_B_local, pcis->is_I_local, MAT_INITIAL_MATRIX, &A_BI));
        PetscCall(PetscObjectReference((PetscObject)pcis->A_II));
        A_II = pcis->A_II;
      }
      PetscCall(MatCreateSchurComplement(A_II, A_II, A_IB, A_BI, pcis->A_BB, &fetidppc_ctx->S_j));

      /* propagate settings of solver */
      PetscCall(MatSchurComplementGetKSP(fetidppc_ctx->S_j, &sksp));
      PetscCall(KSPGetType(pcis->ksp_D, &ksptype));
      PetscCall(KSPSetType(sksp, ksptype));
      PetscCall(KSPGetPC(pcis->ksp_D, &pc));
      PetscCall(PetscObjectTypeCompare((PetscObject)pc, PCSHELL, &isshell));
      if (!isshell) {
        MatSolverType solver;
        PCType        pctype;

        PetscCall(PCGetType(pc, &pctype));
        PetscCall(PCFactorGetMatSolverType(pc, &solver));
        PetscCall(KSPGetPC(sksp, &pc));
        PetscCall(PCSetType(pc, pctype));
        if (solver) PetscCall(PCFactorSetMatSolverType(pc, solver));
      } else {
        PetscCall(KSPGetPC(sksp, &pc));
        PetscCall(PCSetType(pc, PCLU));
      }
      PetscCall(MatDestroy(&A_II));
      PetscCall(MatDestroy(&A_IB));
      PetscCall(MatDestroy(&A_BI));
      PetscCall(MatGetOptionsPrefix(fetimat, &prefix));
      PetscCall(KSPSetOptionsPrefix(sksp, prefix));
      PetscCall(KSPAppendOptionsPrefix(sksp, "harmonic_"));
      PetscCall(KSPSetFromOptions(sksp));
      if (reuse) {
        PetscCall(KSPSetPC(sksp, sub_schurs->reuse_solver->interior_solver));
        PetscCall(PetscObjectIncrementTabLevel((PetscObject)sub_schurs->reuse_solver->interior_solver, (PetscObject)sksp, 0));
      }
    } else { /* default Dirichlet preconditioner is pde-harmonic */
      PetscCall(MatCreateSchurComplement(pcis->A_II, pcis->A_II, pcis->A_IB, pcis->A_BI, pcis->A_BB, &fetidppc_ctx->S_j));
      PetscCall(MatSchurComplementSetKSP(fetidppc_ctx->S_j, pcis->ksp_D));
    }
  } else {
    PetscCall(PetscObjectReference((PetscObject)pcis->A_BB));
    fetidppc_ctx->S_j = pcis->A_BB;
  }
  /* saddle-point */
  if (mat_ctx->xPg) {
    PetscCall(PetscObjectReference((PetscObject)mat_ctx->xPg));
    fetidppc_ctx->xPg = mat_ctx->xPg;
    PetscCall(PetscObjectReference((PetscObject)mat_ctx->yPg));
    fetidppc_ctx->yPg = mat_ctx->yPg;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode FETIDPMatMult_Kernel(Mat fetimat, Vec x, Vec y, PetscBool trans)
{
  FETIDPMat_ctx mat_ctx;
  PC_BDDC      *pcbddc;
  PC_IS        *pcis;

  PetscFunctionBegin;
  PetscCall(MatShellGetContext(fetimat, &mat_ctx));
  pcis   = (PC_IS *)mat_ctx->pc->data;
  pcbddc = (PC_BDDC *)mat_ctx->pc->data;
  /* Application of B_delta^T */
  PetscCall(VecSet(pcis->vec1_B, 0.));
  PetscCall(VecScatterBegin(mat_ctx->l2g_lambda, x, mat_ctx->lambda_local, INSERT_VALUES, SCATTER_REVERSE));
  PetscCall(VecScatterEnd(mat_ctx->l2g_lambda, x, mat_ctx->lambda_local, INSERT_VALUES, SCATTER_REVERSE));
  PetscCall(MatMultTranspose(mat_ctx->B_delta, mat_ctx->lambda_local, pcis->vec1_B));

  /* Add contribution from saddle point */
  if (mat_ctx->l2g_p) {
    PetscCall(VecScatterBegin(mat_ctx->l2g_p, x, mat_ctx->vP, INSERT_VALUES, SCATTER_REVERSE));
    PetscCall(VecScatterEnd(mat_ctx->l2g_p, x, mat_ctx->vP, INSERT_VALUES, SCATTER_REVERSE));
    if (pcbddc->switch_static) {
      if (trans) {
        PetscCall(MatMultTranspose(mat_ctx->B_BI, mat_ctx->vP, pcis->vec1_D));
      } else {
        PetscCall(MatMult(mat_ctx->Bt_BI, mat_ctx->vP, pcis->vec1_D));
      }
    }
    if (trans) {
      PetscCall(MatMultTransposeAdd(mat_ctx->B_BB, mat_ctx->vP, pcis->vec1_B, pcis->vec1_B));
    } else {
      PetscCall(MatMultAdd(mat_ctx->Bt_BB, mat_ctx->vP, pcis->vec1_B, pcis->vec1_B));
    }
  } else {
    if (pcbddc->switch_static) PetscCall(VecSet(pcis->vec1_D, 0.0));
  }
  /* Application of \widetilde{S}^-1 */
  PetscCall(PetscArrayzero(pcbddc->benign_p0, pcbddc->benign_n));
  PetscCall(PCBDDCApplyInterfacePreconditioner(mat_ctx->pc, trans));
  PetscCall(PetscArrayzero(pcbddc->benign_p0, pcbddc->benign_n));
  PetscCall(VecSet(y, 0.0));
  /* Application of B_delta */
  PetscCall(MatMult(mat_ctx->B_delta, pcis->vec1_B, mat_ctx->lambda_local));
  /* Contribution from boundary pressures */
  if (mat_ctx->C) {
    const PetscScalar *lx;
    PetscScalar       *ly;

    /* pressure ordered first in the local part of x and y */
    PetscCall(VecGetArrayRead(x, &lx));
    PetscCall(VecGetArray(y, &ly));
    PetscCall(VecPlaceArray(mat_ctx->xPg, lx));
    PetscCall(VecPlaceArray(mat_ctx->yPg, ly));
    if (trans) {
      PetscCall(MatMultTranspose(mat_ctx->C, mat_ctx->xPg, mat_ctx->yPg));
    } else {
      PetscCall(MatMult(mat_ctx->C, mat_ctx->xPg, mat_ctx->yPg));
    }
    PetscCall(VecResetArray(mat_ctx->xPg));
    PetscCall(VecResetArray(mat_ctx->yPg));
    PetscCall(VecRestoreArrayRead(x, &lx));
    PetscCall(VecRestoreArray(y, &ly));
  }
  /* Add contribution from saddle point */
  if (mat_ctx->l2g_p) {
    PetscCall(VecISSet(pcis->vec1_B, mat_ctx->lP_B, 0));
    if (trans) {
      PetscCall(MatMultTranspose(mat_ctx->Bt_BB, pcis->vec1_B, mat_ctx->vP));
    } else {
      PetscCall(MatMult(mat_ctx->B_BB, pcis->vec1_B, mat_ctx->vP));
    }
    if (pcbddc->switch_static) {
      PetscCall(VecISSet(pcis->vec1_D, mat_ctx->lP_I, 0));
      if (trans) {
        PetscCall(MatMultTransposeAdd(mat_ctx->Bt_BI, pcis->vec1_D, mat_ctx->vP, mat_ctx->vP));
      } else {
        PetscCall(MatMultAdd(mat_ctx->B_BI, pcis->vec1_D, mat_ctx->vP, mat_ctx->vP));
      }
    }
    PetscCall(VecScatterBegin(mat_ctx->l2g_p, mat_ctx->vP, y, ADD_VALUES, SCATTER_FORWARD));
    PetscCall(VecScatterEnd(mat_ctx->l2g_p, mat_ctx->vP, y, ADD_VALUES, SCATTER_FORWARD));
  }
  PetscCall(VecScatterBegin(mat_ctx->l2g_lambda, mat_ctx->lambda_local, y, ADD_VALUES, SCATTER_FORWARD));
  PetscCall(VecScatterEnd(mat_ctx->l2g_lambda, mat_ctx->lambda_local, y, ADD_VALUES, SCATTER_FORWARD));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode FETIDPMatMult(Mat fetimat, Vec x, Vec y)
{
  PetscFunctionBegin;
  PetscCall(FETIDPMatMult_Kernel(fetimat, x, y, PETSC_FALSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode FETIDPMatMultTranspose(Mat fetimat, Vec x, Vec y)
{
  PetscFunctionBegin;
  PetscCall(FETIDPMatMult_Kernel(fetimat, x, y, PETSC_TRUE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode FETIDPPCApply_Kernel(PC fetipc, Vec x, Vec y, PetscBool trans)
{
  FETIDPPC_ctx pc_ctx;
  PC_IS       *pcis;

  PetscFunctionBegin;
  PetscCall(PCShellGetContext(fetipc, &pc_ctx));
  pcis = (PC_IS *)pc_ctx->pc->data;
  /* Application of B_Ddelta^T */
  PetscCall(VecScatterBegin(pc_ctx->l2g_lambda, x, pc_ctx->lambda_local, INSERT_VALUES, SCATTER_REVERSE));
  PetscCall(VecScatterEnd(pc_ctx->l2g_lambda, x, pc_ctx->lambda_local, INSERT_VALUES, SCATTER_REVERSE));
  PetscCall(VecSet(pcis->vec2_B, 0.0));
  PetscCall(MatMultTranspose(pc_ctx->B_Ddelta, pc_ctx->lambda_local, pcis->vec2_B));
  /* Application of local Schur complement */
  if (trans) {
    PetscCall(MatMultTranspose(pc_ctx->S_j, pcis->vec2_B, pcis->vec1_B));
  } else {
    PetscCall(MatMult(pc_ctx->S_j, pcis->vec2_B, pcis->vec1_B));
  }
  /* Application of B_Ddelta */
  PetscCall(MatMult(pc_ctx->B_Ddelta, pcis->vec1_B, pc_ctx->lambda_local));
  PetscCall(VecSet(y, 0.0));
  PetscCall(VecScatterBegin(pc_ctx->l2g_lambda, pc_ctx->lambda_local, y, ADD_VALUES, SCATTER_FORWARD));
  PetscCall(VecScatterEnd(pc_ctx->l2g_lambda, pc_ctx->lambda_local, y, ADD_VALUES, SCATTER_FORWARD));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode FETIDPPCApply(PC pc, Vec x, Vec y)
{
  PetscFunctionBegin;
  PetscCall(FETIDPPCApply_Kernel(pc, x, y, PETSC_FALSE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode FETIDPPCApplyTranspose(PC pc, Vec x, Vec y)
{
  PetscFunctionBegin;
  PetscCall(FETIDPPCApply_Kernel(pc, x, y, PETSC_TRUE));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode FETIDPPCView(PC pc, PetscViewer viewer)
{
  FETIDPPC_ctx pc_ctx;
  PetscBool    isascii;
  PetscViewer  sviewer;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
  if (isascii) {
    PetscMPIInt rank;
    PetscBool   isschur, isshell;

    PetscCall(PCShellGetContext(pc, &pc_ctx));
    PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank));
    PetscCall(PetscObjectTypeCompare((PetscObject)pc_ctx->S_j, MATSCHURCOMPLEMENT, &isschur));
    if (isschur) {
      PetscCall(PetscViewerASCIIPrintf(viewer, "  Dirichlet preconditioner (just from rank 0)\n"));
    } else {
      PetscCall(PetscViewerASCIIPrintf(viewer, "  Lumped preconditioner (just from rank 0)\n"));
    }
    PetscCall(PetscViewerGetSubViewer(viewer, PetscObjectComm((PetscObject)pc_ctx->S_j), &sviewer));
    if (rank == 0) {
      PetscCall(PetscViewerPushFormat(sviewer, PETSC_VIEWER_ASCII_INFO));
      PetscCall(PetscViewerASCIIPushTab(sviewer));
      PetscCall(MatView(pc_ctx->S_j, sviewer));
      PetscCall(PetscViewerASCIIPopTab(sviewer));
      PetscCall(PetscViewerPopFormat(sviewer));
    }
    PetscCall(PetscViewerRestoreSubViewer(viewer, PetscObjectComm((PetscObject)pc_ctx->S_j), &sviewer));
    PetscCall(PetscObjectTypeCompare((PetscObject)pc_ctx->B_Ddelta, MATSHELL, &isshell));
    if (isshell) {
      BDdelta_DN ctx;
      PetscCall(PetscViewerASCIIPrintf(viewer, "  FETI-DP BDdelta: DB^t * (B D^-1 B^t)^-1 for deluxe scaling (just from rank 0)\n"));
      PetscCall(MatShellGetContext(pc_ctx->B_Ddelta, &ctx));
      PetscCall(PetscViewerGetSubViewer(viewer, PetscObjectComm((PetscObject)pc_ctx->S_j), &sviewer));
      if (rank == 0) {
        PetscInt tl;

        PetscCall(PetscViewerASCIIGetTab(sviewer, &tl));
        PetscCall(PetscObjectSetTabLevel((PetscObject)ctx->kBD, tl));
        PetscCall(KSPView(ctx->kBD, sviewer));
        PetscCall(PetscViewerPushFormat(sviewer, PETSC_VIEWER_ASCII_INFO));
        PetscCall(MatView(ctx->BD, sviewer));
        PetscCall(PetscViewerPopFormat(sviewer));
      }
      PetscCall(PetscViewerRestoreSubViewer(viewer, PetscObjectComm((PetscObject)pc_ctx->S_j), &sviewer));
    }
    PetscCall(PetscViewerFlush(viewer));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}